Question

Science Q6 M. ABCD is a cyclic quadrilateral with AC = AD = CD = 3 cm, AB = 2 cm and BD = 4 cm, find the perimeter of quadrilateral ABCD. 7 cm 9 cm 10 cm 13 cm 01​

Answer 1

Answer:

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Step-by-step explanation:

so as quadrilateral abcd is a cyclic quadrilateral

we can apply here ptolemy' s theorem which states that in a cyclic quadrilateral the sum of product of its opposite sides is equal to product of its diagonals

so thus

we get

(AB×CD)+(BC×AD)=(AC×BD)

so substitute given sides in above geometric equation

we get

(2×3)+3BC=(3×4)

ie 3BC=12-6

so 3BC=6

ie BC=2 cm

so thus perimter of cyclic quadrilateral ABCD=

AB+BC+CD+AD

=2+2+3+4

=4+6

=10 cm

thus option c ie 10 cm is ryt